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\begin{equation*}\int\frac{dx}{x^2-a^2} = -\frac{1}{a}\,\mathrm{arcoth}\frac{x}{a} = \frac{1}{2a}\ln\frac{x-a}{x+a} \qquad\mbox{(for }|x| > |a|\mbox{)}\,\!\end{equation*}
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